# Single-Molecule Conductance Theory Using Different Orbitals for Different Spins: Applications to π-Electrons in Graphene Molecules

## Abstract

In the present paper, we consider many-body π-electron models and computational tools for treating single-molecule conductance in middle-size graphene molecules. Our study highlights the importance of accounting for long-range interactions and electron-correlation effects which are crucial for a correct description of electron transmission in conjugated systems. Here we construct one-electron Green’s function matrix for the half-projected Hartree-Fock method implementing the different orbitals for different spins (DODS) approach. Moreover, the simplified DODS in the form of quasi-correlated tight-binding (QCTB) and related models are invoked. We compare these electron-correlation models with the usual tight-binding (TB) approximation and show that TB is actually incorrect as a single-molecule conductance theory of graphenic and similar structures. In our specific applications, we calculate the conductance spectra for small graphene nanoflakes and find, in particular, that “zigzag” connections can afford significantly higher electron transmission than “armchair” connections.

## Abbreviations

- AO
Atomic orbital

- DODS
Different orbitals for different spins

- EHF
Extended Hartree-Fock

- FCI
Full configuration interaction

- GF
Green’s function

- GQD
Graphene quantum dot

- HPHF
Half-projected Hartree-Fock

- MO
Molecular orbital

- MSE
Molecular-scale electronics

- QCLRI
Quasi-correlated long-range interaction

- QCTB
Quasi-correlated tight-binding (model)

- RHF
Restricted Hartree-Fock

- TB
Tight-binding (model)

- UHF
Unrestricted Hartree-Fock

- WBL
Wide-band limit

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